1. Divide the number repeatedly by 2:
Keep track of each remainder.
We stop when we get a quotient that is equal to zero.
- division = quotient + remainder;
- 21 389 182 899 ÷ 2 = 10 694 591 449 + 1;
- 10 694 591 449 ÷ 2 = 5 347 295 724 + 1;
- 5 347 295 724 ÷ 2 = 2 673 647 862 + 0;
- 2 673 647 862 ÷ 2 = 1 336 823 931 + 0;
- 1 336 823 931 ÷ 2 = 668 411 965 + 1;
- 668 411 965 ÷ 2 = 334 205 982 + 1;
- 334 205 982 ÷ 2 = 167 102 991 + 0;
- 167 102 991 ÷ 2 = 83 551 495 + 1;
- 83 551 495 ÷ 2 = 41 775 747 + 1;
- 41 775 747 ÷ 2 = 20 887 873 + 1;
- 20 887 873 ÷ 2 = 10 443 936 + 1;
- 10 443 936 ÷ 2 = 5 221 968 + 0;
- 5 221 968 ÷ 2 = 2 610 984 + 0;
- 2 610 984 ÷ 2 = 1 305 492 + 0;
- 1 305 492 ÷ 2 = 652 746 + 0;
- 652 746 ÷ 2 = 326 373 + 0;
- 326 373 ÷ 2 = 163 186 + 1;
- 163 186 ÷ 2 = 81 593 + 0;
- 81 593 ÷ 2 = 40 796 + 1;
- 40 796 ÷ 2 = 20 398 + 0;
- 20 398 ÷ 2 = 10 199 + 0;
- 10 199 ÷ 2 = 5 099 + 1;
- 5 099 ÷ 2 = 2 549 + 1;
- 2 549 ÷ 2 = 1 274 + 1;
- 1 274 ÷ 2 = 637 + 0;
- 637 ÷ 2 = 318 + 1;
- 318 ÷ 2 = 159 + 0;
- 159 ÷ 2 = 79 + 1;
- 79 ÷ 2 = 39 + 1;
- 39 ÷ 2 = 19 + 1;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
21 389 182 899(10) = 100 1111 1010 1110 0101 0000 0111 1011 0011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 35.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
The first bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number
The least number that is:
1) a power of 2
2) and is larger than the actual length, 35,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64:
Number 21 389 182 899(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
21 389 182 899(10) = 0000 0000 0000 0000 0000 0000 0000 0100 1111 1010 1110 0101 0000 0111 1011 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.